# 4. Find the equation of a line parallel to x-axis and passing through the origin.

Equation of a line parallel to the x-axis and passing through the origin $(0,0,0)$ is itself x-axis.

So, let A be a point on the x-axis.

Therefore, the coordinates of A are given by $(a,0,0)$, where $a\epsilon R$.

Now, the direction ratios of OA are $(a-0) =a,0 , 0$

So, the equation of OA is given by,

$\frac{x-0}{a} = \frac{y-0}{0} = \frac{z-0}{0}$

or  $\Rightarrow \frac{x}{1} = \frac{y}{0} = \frac{z}{0} = a$

Thus, the equation of the line parallel to the x-axis and passing through origin is

$\frac{x}{1} = \frac{y}{0} = \frac{z}{0}$

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